# Definition:Antihomomorphism/Group Antihomomorphism

## Definition

Let $\struct {S, \circ}$ and $\struct {T, *}$ be groups.

Then $\phi: S \to T$ is a group antihomomorphism if and only if:

$\forall x, y \in S:\map \phi {x \circ y} = \map \phi y * \map \phi x$